Trigonometric Equation Solving Quiz

The video tutorial explains how to solve the trigonometric equation sine x = -0.32 within the interval from 0 to 2π. It highlights that the sine function is negative in the third and fourth quadrants. The tutorial demonstrates using a graphing calculator to find the inverse sine of -0.32, resulting in a negative angle. It then explains how to adjust this angle to find solutions within the specified interval, focusing on the fourth and third quadrants. The tutorial concludes by providing the two solutions and emphasizes entering them in order of size.

In which quadrants is the sine function negative?

• First and Second

• Second and Third

• Third and Fourth

• First and Fourth

What is the first step when using a calculator to solve sin(x) = -0.32?

• Switch to Radian mode

• Switch to Degree mode

• Find the cosine of the angle

• Find the tangent of the angle

What is the approximate value of the angle given by the calculator for sin(x) = -0.32?

• 0.3257 radians

• -0.3257 radians

• -1.3257 radians

• 1.3257 radians

How do you adjust the negative angle to find the fourth quadrant angle in the interval 0 to 2π?

• Add π radians

• Subtract π radians

• Add 2π radians

• Subtract 2π radians

What is the approximate value of the fourth quadrant angle in radians?

• 3.4673 radians

• 4.9575 radians

• 5.9575 radians

• 2.4673 radians

What is the reference angle used to find the third quadrant angle?

• 3.3257 radians

• 2.3257 radians

• 1.3257 radians

• 0.3257 radians

How do you calculate the third quadrant angle using the reference angle?

• Add the reference angle to π radians

• Subtract the reference angle from 2π radians

• Subtract the reference angle from π radians

• Add the reference angle to 2π radians

What is the approximate value of the third quadrant angle in radians?

• 4.4673 radians

• 2.4673 radians

• 5.4673 radians

• 3.4673 radians

Which angle should be entered first for the homework?

• The larger angle

• The smaller angle

• The angle in the first quadrant

• The angle in the second quadrant

What is the importance of the reference angle in solving trigonometric equations?

• It helps find the exact value of sine

• It determines the quadrant of the angle

• It is used to find angles with the same sine value

• It is used to convert radians to degrees